The Tully-Fischer method relies on being able to relate the mass of a galaxy to its rotation velocity. Stars in the outer-most regions of the Milky Way galaxy, located at a distance of 50 kpc from the galactic centre, are observed to orbit at a speed rot = 250 km s-¹. Using Kepler's 3rd Law, determine the mass in the Milky Way that lies interior to 50 kpc. Express your answer in units of the Solar mass.
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- If you find a galaxy that is the same size and mass as our Milky Way Galaxy, what orbital velocity would a small satellite galaxy have if it orbits 51 kpc from the center of the larger galaxy? (Assume the total mass of our galaxy is about 4.0 1011 solar masses, M.)The Algol binary system consists of a 3.7 Msun star and a 0.8 Msun star with an orbital period of 2.87 days. Using Newton’s version of Kepler’s Third Law, calculate the distance, a, between the two stars. Compare that to the size of Betelgeuse (you’ll need to look that up). Newton’s Version of Kepler’s Law: (M1 + M2) P2 = (4p2 /G) a3 Rearrange the equation to solve for a. Pi, p, is equal to 3.14. IMPORTANT NOTE: Google the value of G (the Universal Gravitational Constant) or look it up in your text. NOTICE THE UNITS. You must convert every distance and time in your equation to the same units, otherwise, you’ll get an incorrect answer. That means you must convert distances to meters, solar masses to kilograms, and time to seconds. When you compare your value to the size of Betelgeuse, it will also help that they are in the same units.The surface mass density of the disk of a galaxy is given in the provided image. Σ0 is the central surface density and Rd is the scale-length, and they are both constant. Find the total mass (M) of the disk in terms of Σ0 and Rd.
- Most of the dark matter in a galaxy is located in a galaxy's (hint: one word) which allows the luminous matter, particularly near the outer edges of the galaxy, to rotate around the center of the galaxy at a faster speed than predicted by Kepler's 3rd Law.If a galaxy is 8.8 Mpc away from Earth and recedes at 498 km/s, what is H0 (in km/s/Mpc)? _______ km/s/Mpc What is the Hubble time (in yr)? _______ yr How would acceleration change your answer? A: If the expansion of the Universe has been accelerating, the Universe could be substantially younger than the value entered above. B: If the expansion of the Universe has been accelerating, the Universe could be substantially older than the value entered above.Pretend that galaxies are spaced evenly, 7.0 Mpc apart, and the average mass of a galaxy is 1.0 ✕ 1011 M. What is the average density (in kg/m3) of matter in the universe? (Note: The volume of a sphere is 4/3pieR^3 and the mass of the sun is 2.0 ✕ 1030 kg.) ______ kg/m^3 Which model universe does this density value support? A: open B: flat C: closed
- Based on comparison with the Moon, it can be calculated that Andromeda would have to have a diameter of 35,000 km if it were at the same distance from us as the Moon. But it turns out that the distance from Earth to the Andromeda galaxy has been measured to be 6 × 1013 times farther than to the Moon. That's 60 trillion times farther. What is the true diameter of Andromeda, based on these numbers?If a galaxy is 9.0 Mpc away from Earth and recedes at 510 km/s, what is H? What is the Hubble time?Globular clusters revolve around the Galaxy in highly elliptical orbits. Where would you expect the clusters to spend most of their time? (Think of Kepler’s laws.) At any given time, would you expect most globular clusters to be moving at high or low speeds with respect to the center of the Galaxy? Why? (If you would like to learn more about globular clusters, read Section 22.2 of the book, though it is not necessary to answer this question)
- The gas in the outer region of the Andromeda galaxy is found to be orbiting the galaxy with a velocity of 250 km/s. The gas is at a distance of 35 kpc from the center of the galaxy. The total mass of the galaxy is _______ solar masses.The surface brightness profiles of elliptical galaxies follow the Sersic formula with n = 4. How much fainter is the elliptical galaxy at a radius of r compared r0 (the radius at which the brightness falls off by a factor of e), or in other words, what is the ratio of I(r)/I0. Values: r = 14 r0The Sun is moving at 220 ??/? around the Galactic Center at a more-or-less constant distance of 8.5 ???. To appreciate how remarkable this is, consider the following questions: a) How massive would the Sun have to be for the Earth to have an orbital velocity of 220 km/s at 1 AU? b) How fast would the Earth move if it was in orbit around the Sun at a distance of 8.5 kpc? Of course, you may ignore the effects of all other stars in this calculation.